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We present high angular resolution (0.3" or 37 pc) Atacama LargeMillimeter/sub-millimeter Array (ALMA) observations of the CO(2-1) lineemission from a central disc in the early-type galaxy NGC 524. This disc isshown to be dynamically relaxed, exhibiting ordered rotation about a compact1.3mm continuum source, which we identify as emission from an activesupermassive black hole (SMBH). There is a hole at the centre of the discslightly larger than the SMBH sphere of influence. An azimuthal distortion ofthe observed velocity field is found to be due to either a position angle warpor radial gas flow over the inner 2.5". By forward-modelling the observations,we obtain an estimate of the SMBH mass of$4.0^{+3.5}_{-2.0}\times10^8\,\mathrm{M_\odot}$, where the uncertainties are atthe $3\sigma$ level. The uncertainties are dominated by the poorly constrainedinclination and the stellar mass-to-light ratio of this galaxy, and ourmeasurement is consistent with the established correlation between SMBH massand stellar velocity dispersion. Our result is roughly half that of theprevious stellar dynamical measurement, but is consistent within theuncertainties of both. We also present and apply a new tool for modellingcomplex molecular gas distributions.

WISDOM project - IV. A molecular gas dynamical measurement of the supermassive black hole mass in NGC 524